Research On Linear Matrix Inequality Based Nonlinear Model Predictive Control

Nonlinear model predictive control (NMPC) is an important branch of control theory. After twenty years of development, much progress has been made in NMPC and some theory has reached a relative mature stage. While, comparing with the great success in the applications of the linear model predictive control, few applications of NMPC have been reported. This may attributes to the complexcity of NMPC, and some fundamental problems of NMPC theory have not been well resolved yet. Among them, the problems of stability, robustness and efficiency of the optimization are the main three ones, and make the main obstacles in the applications of NMPC. So the current NMPC researches still focus on the problems of stability, robust, and optimization efficiency.In this thesis the linear matrix inequality (LMI) is used as the main design tool to study the above problems in NMPC. While by integrating LMI into NMPC, it may make the applicable domain very small. This thesis gives a detailed analysis about this problem and presents a series of resolving methods, which afford a new way in NMPC research.In this thesis, the background, current research condition and future direction of NMPC is first reviewed. And as the preliminary knowledge, LMI is introduced, including its definition, main problem and its optimal algorithm.Then the general concept of designing NMPC algorithm with LMI is introduced. As the discussions pointed, two reasons mainly account for the small applicable domain of this class algorithms. One is the stable constraints are too strong, and the other is the polynomial model representation of nonlinear systems is too conservative.Aiming at the first problem, a parameterized algorithm is proposed in chapter 2, which can enlarge the applicable domain efficiently by tuning the parameters. In chapter 3, a feasible solution based LMI NMPC algorithm is proposed. For the optimal solution in NMPC is usually difficult to achieved, using feasible solution can loosen the To the second problem, multi-model method is integrated in NMPC in chapter 4, and a multi-model and LMI based NMPC algorithm is proposed. In this method, after delicately design for local controllers, the stability after switching controllers can be guaranteed.In this thesis, the concept of using extended LMI in NMPC design is also introduced. For the extended LMI has many good properties, such as smaller conservativeness and more agilities in design, two or more optimal index can be achieved simultaneously while the conservativeness is not enlarged.In this thesis, MPC and LMI is also used in the greenhouse environment system control, and in chapter 6, the new modeling method and MPC method is proposed which are based on the switching system control.In this thesis, all the proposed algorithms are detailed analyzed and most of the theorems are proved. And some simulated experiments are given to illuminate the effectiveness of algorithms.